Home
Class 10
MATHS
Prove that the points (a, a), (-a, -a) a...

Prove that the points `(a, a), (-a, -a) and (-asqrt(3), asqrt(3))` are the vertices of an equilateral triangle.

Text Solution

Verified by Experts

Let the points are `A(a,a),B(-a, -a) and C(-a sqrt(3), asqrt(3))`.
`therefore " "AB=sqrt ((-a-a)^(2)+(-a -a)^(2))=sqrt ((-2 a)^(2)+(-2a)^(2))`
` " "=sqrt( 4a^(2)+4a^(2))=sqrt (8a^(2))=2sqrt(2)a`
` " "BC=sqrt((-asqrt(3)+a^(2))+(asqrt(3)+a^(2)))`
` " "=sqrt (3a^(2)+a^(2)-2sqrt(3)a^(2)+3a^(2)+ a^(2)+2sqrt(3)a^(2))= sqrt(8a^(2))=2sqrt(2) a`
and `" "CA=sqrt((-asqrt(3)-a)^(2)+(asqrt(3)-a)^(2))`
`" "=sqrt (3a^(2)+a^(2)+2sqrt(3)a^(2)+3a^(2)+a^(2)- 2sqrt(3)a^(2))`
`" "=sqrt(8a^(2))=2sqrt(2)a`
` because" "AB=BC=CA`
`thereforeDelta ABC` is an equilateral triangle.
Promotional Banner

Topper's Solved these Questions

  • CO-ORDINATE GEOMETRY

    NAGEEN PRAKASHAN|Exercise Miscellaneous Examples|8 Videos

  • CO-ORDINATE GEOMETRY

    NAGEEN PRAKASHAN|Exercise Problems Of NCERT/exemplar|14 Videos

  • CIRCLES

    NAGEEN PRAKASHAN|Exercise Revision Exercise Long Answer Questions|3 Videos

  • CONSTRUCTIONS

    NAGEEN PRAKASHAN|Exercise PROBLEMS FROM NCERT/ EXEMPLAR|10 Videos

Similar Questions

Explore conceptually related problems

Prove that the points (2a, 4a), (2a, 6a) and (2a+ sqrt(3) a, 5a) are the vertices of an equilateral triangle.

Show that the points (-3, -3), (3, 3) and (-3sqrt(3), 3sqrt(3)) are the vertices of an equilateral triangle.

Show that the points (a,a),(-a,-a) and (-sqrt(3)a,sqrt(3)a) are the vertices of an equilateral triangle.Also,find its area.

Prove that the points (2a,4a),(2a,6a) and (2a+sqrt(3)a,5a) are the vertices of an equilaterall triangle whose side is 2a

Prove that the points A(2, 4), B(2, 6) and C(2 + sqrt(3) , 5) are the vertices of an equilateral triangle.

Show that the points O(0, 0), A(3, sqrt(3)) "and "B(3, -sqrt(3)) are the vertices of an equilateral triangle. Find the area of this triangle.

Prove that the points (0, 0), (3, (pi)/(2)) and (3, (pi)/(6)) are the vertices of an equilateral triangle.

Using distance formula,prove that the points (-1+sqrt(3)i)/(2) and (-1-sqrt(3)i)/(2) form the vertices of an equilateral triangle in complex plane.

Show that the points A(1,2),B(1,6), C(1 + 2sqrt(3),4) are the vertices of an equilateral triangle .